Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: UNCOUNTABILITY
Replies: 59   Last Post: Dec 24, 2012 2:06 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: UNCOUNTABILITY
Posted: Dec 21, 2012 6:57 PM

On Dec 22, 7:17 am, Virgil <vir...@ligriv.com> wrote:
> In article
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 20 Dez., 22:14, Virgil <vir...@ligriv.com> wrote:
>
> > > In order to claim that the set of reals is countable reals, WM must show
> > > that the set of reals satisfies the definition of countability.

>
> > No, I have shown that the notion of countability is nonsense.
>
> NOt anywhere nearly as clearly as others have shown many of the notions
> of your WMYtheology are nonsense.
>
> Countability has a standard definition: A set S is countable if and only
> if there is an injective mapping from N to S or a surjective mapping
> from S to N, and S is otherwise uncountable.
>

This is all countable subsets of N.

TM1(1) Halts => 1 e POWERSET_1
TM1(2) Loops => 2 !e POWERSET_1
TM1(3) Halts => 3 e POWERSET_1
TM2(1) Halts => 1 e POWERSET_2
TM2(2) Halts => 2 e POWERSET_2
TM2(3) Halts => 3 e POWERSET_2
...

POWERSET(N) = { {1,3,...} {1,2,3...} ... }

1 <=> {1,3,..}
2 <=> {1,2,3,...}
...

What are you guys missing here, you want the 1st million elements of
the 1st million subsets of N printed out??

What method for counting functions do you prefer?

Turing machines?

TM-1
S-00L->S
S-10L->S
TM-2
S-00L->S
S-10R->S
...
TM-8
S-11R->S
S-01R->S
--------
Next comes TM-9, the first 2 State TM.
TM-9
S-00L->1
S-10L->1
1-00L->S
1-10L->S
..

LISP strings? lambda expressions, LR grammar reduction,

my cellular Half-TM computer model?
www.tinyurl.com/blueprints-turing

Unify Fetch cycle, incremental 3GL .EXE files, Supercombinators,
neural nets, ...

What's your preferred computational method for listing all subsets of
N?

Herc

--
S: if stops(S) gosub S
This example proves stops() must be un-computable!
~ George Greene

Date Subject Author
12/19/12 george
12/20/12 Zaljohar@gmail.com
12/20/12 Barb Knox
12/20/12 ross.finlayson@gmail.com
12/20/12 Zaljohar@gmail.com
12/20/12 ross.finlayson@gmail.com
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/20/12 Graham Cooper
12/20/12 mueckenh@rz.fh-augsburg.de
12/20/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 William Hughes
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/22/12 William Hughes
12/22/12 Graham Cooper
12/23/12 Virgil
12/23/12 William Hughes
12/24/12 Graham Cooper
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 William Hughes
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 Virgil
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/21/12 Virgil
12/20/12 Virgil
12/20/12 Graham Cooper
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 Graham Cooper
12/21/12 Graham Cooper